### Brain Teasers

# Cafeteria Capacity

Math
Math brain teasers require computations to solve.

The Madison School has a new cafeteria with very artistic, new tables for its 375 students. Besides the big round tables, some tables are octagons, pentagons, hexagons or squares. The students eat lunch in 3 shifts, with an equal number of students dining during each lunch period. Because the cafeteria is new, they've allowed extra space in case there are more students in the future. Right now, there are 47 empty seats during each lunch period.

Each round table seats ten students. Each of the other types of tables can seat one student on each side.

There are at least 4 tables of each shape.

The same total number of students can be seated at the square tables as at the pentagons, but there are more square tables than pentagons.

The total number of students who can be seated at round tables is equal to the total number of students at the square and pentagon shaped tables combined.

There are more octagonal tables than any other shape.

There is a total of 4 fewer places at the hexagons than at the round tables.

How many tables are there of each shape?

Each round table seats ten students. Each of the other types of tables can seat one student on each side.

There are at least 4 tables of each shape.

The same total number of students can be seated at the square tables as at the pentagons, but there are more square tables than pentagons.

The total number of students who can be seated at round tables is equal to the total number of students at the square and pentagon shaped tables combined.

There are more octagonal tables than any other shape.

There is a total of 4 fewer places at the hexagons than at the round tables.

How many tables are there of each shape?

### Hint

Make a chart, and then guess and check to calculate the total number of places at each type of table.### Answer

There are 4 round tables, 7 octagonal tables, 6 hexagonal tables, 4 pentagonal tables, and 5 square tables.Table Shape Number of Tables Number of Seats Total Seats

square 5 4 20

pentagon 4 5 20

hexagon 6 6 36

octagon 7 8 56

round 4 10 40

Total places 172

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## Comments

that wuz really easy i got it right away

ok thanx for your comment

That was good, but I came up with the answer in a different way:

Round 5x10=50

octagon 8x7=56

pentagon 5x4=20

hexagon 5x6=30

square 4x4=16

Round 5x10=50

octagon 8x7=56

pentagon 5x4=20

hexagon 5x6=30

square 4x4=16

creative solution

Good one; fairly easy, but made me think. I enjoy this type of puzzle. Thanks a lot. (We know that your answer is the only correct one)

Jul 04, 2005

okai. took me awhile, had to write everything down on paper. BUt i got got it! i love problem solving. xept for when you HAVE to do it. lol. anyhoo that was lots of fun. liked it alot. by the way, cute name!

thanx karma

thanks coolperson

especially for the last part of your comment

thanks coolperson

especially for the last part of your comment

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This had the makings of a good teaser, but fell a little short.

The clue that there are more square tables than pentagons is redundant since they seat the same number. You can eliminate the clue regarding the octagon tables since the next possible solution for the rest of the tables is double the number, which is more than the 172.

Removing the unnecessary information would add a little kick to the teaser.

The clue that there are more square tables than pentagons is redundant since they seat the same number. You can eliminate the clue regarding the octagon tables since the next possible solution for the rest of the tables is double the number, which is more than the 172.

Removing the unnecessary information would add a little kick to the teaser.

I don't get it... Why is the answer 172? Where does that number come from? Shouldn't it be closer to 375... or 422?

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